MATH 8001 MATH 8001 February 17, 2012 February 17, 2012 How to write and deliver a (ahem) lecture How to write and deliver a lecture to a large class of pre- calculus or calculus students for the first time We’ll save discussion of managing a lecture course for March 30. Any issues arising in your current teaching? Untackled topics from 10 February - Krantz’s opinion is that students should not hire tutors. Agree? - Krantz seems to suggest that lecturers may be at an advantage if they have never been a TA. Agree? - Final A ⇒ Course A? - Do students really read posted solutions? - What are the e ff ects of not collecting and grading homework? Are quizzes a suitable alternative?
Plan for today: Golden rule: Be yourself. Students keenly detect discomfort. • Tips on crowd control • Mathematical content issues: preparation, organization, the- ory/examples, pacing. . . First day Crowd control - It is important to create a good first impression and set a 1. “Own the room”. Walk to the back before class. business-like tone. Fill the room with your voice. If necessary, use a microphone, - It is easier to relax a business-like environment later than it is and in that case, bring batteries every day. Imagine speaking to rein in an unruly environment. with a person in the back row. - For the beginning (only) of the first day, write out a script. Then it will be easier to talk extemporaneously when you are in the flow of the mathematics.
Crowd control Crowd control 2. Be prompt so that the students will too. 3. When students are anonymous, they are less likely to feel personal responsibility for their behavior. - Start at the o ffi cial time everyday, using a room clock or a laptop clock. There are 15 minutes between classes, so there should be plenty of time to prepare technology and boards. - Choose a handful to names to call at the beginning of class. - “It disrupts the other students if you leave before the end of - Urge them to visit your o ffi ce hour, if only briefly. the time.” Emphasize their obligation to each other, not your irritation with them. Tell them to inform you before class if they - Stop by your students’ discussion sections. intend to leave early, and ask them to sit in the back row. - If you are in the middle of something at the end of the time - Chat with students before class. (something you should try not to do), say “I need one minute to finish this idea” or “I will return to this example at the beginning of next time” (and then do it). Crowd control Crowd control 4. Electronic distractions 5. Eye contact - Make clear on the first day that cell phones, music players, and - Lack of eye contact indicates nervousness. laptops should be turned o ff , and be willing to enforce it. - Make eye contact with people in the back row – everyone will - I find that meaningful eye contact is most e ff ective in curbing see that you are making eye contact with someone. Do not stare this behavior; students do not like to be singled out in class. at the ceiling. - These eye contact breaks allow you to check how students are keeping up with your pace.
Content considerations Content considerations 1. PREPARE. Make it worth the students’ time to attend. 2. I recommend using slides from a laptop or on an overhead projector. - In particular, try not to work out solutions for the first time on the spot. The most common loss of time and loss of focus of - Not complete details (the pace will be too fast for note-takers) students is due to trying to fix solutions gone awry. If you do get lost – and it will happen – say that you will move on and - Instead, use slides to give an outline and statements of defini- provide that solution later. tions, theorems, examples, and exercises. Write details on the board. Content considerations Content considerations 3. Write with the large chalk (if in a room with chalkboards). 4. Asking questions Bring this with you every day – there is a supply in the mail room. Or, bring fresh dry-erase markers every day. - Questions like “Does everyone understand?” don’t elicit re- sponses, and easy questions that require numerical answers don’t - Walk to the back of the room to check that your writing is either, and can be viewed as insulting. legible. Also, this breaks the barrier with the students. - Better to ask questions like “What do I do now?” or “Why - Include only the most important information in a graph, and wouldn’t approach x work here?” draw graphs as large as possible. - Be willing to wait what seems like a long time for someone to volunteer the answer. This can be a good time to walk up the aisles. It also gives careful note takers time to catch up.
Content considerations Content considerations 5. Soliciting questions 6. Change the pace and activities to improve attention - “Does anyone have any questions?” Wait for responses. - One suggestion: halfway through class, give a short exercise, and ask students to compare solutions with their neighbors. - Walk to the person asking the question. - Asking a student to come to the board to give a solution is - Most important: REPEAT THE QUESTION for the whole rarely e ff ective, but it can be useful (once) to demonstrate that audience to hear (paraphrasing if necessary to clarify or focus you welcome students’ input. Only after a student volunteers the question. an answer aloud. I don’t recommend cold-calling students in lectures (or anywhere, really). - Be willing to tell a student “That’s an important question, but it is too specific to spend time on during lecture. I will be happy to answer your question after class.” Content considerations Content considerations 7. We overestimate students’ tolerance for lists of theorems, 8. Look for one take-home idea to emphasize at the beginning mathematical formalism, ∀ , ∃ , ∈ , etc. and end. Students want to know, practically and mathematically, “Why is this important for me to know?”
Content considerations Content considerations 9. Near the end of the period, it is better to summarize than to 10. Organization: “top to bottom” or “bottom to top”? start a new idea or example that you can’t finish. Start with examples to motivate general idea, or start with gen- eral idea? Showing applications of a theorem before providing a justification for the theorem. Content considerations Assignment, due Friday, February 24 11. Help students who are taking notes and not processing any information: give clear markers for the beginning and end of Write a set of lecture notes for one 50-minute lecture on a text- examples, use boxes for important ideas, extended pauses to book section that your current course will be covering next week. make transitions. Write notes that you would take to give the lecture, but make sure they’re detailed enough that you would make them available for students afterward. Pay close attention to length – mark where you are likely to finish.
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